Harmonic and arithmetic means

The local Utah Department of Child Service office wants to project staffing needs based on current social worker assignments. They have the number of cases per social worker for the following staff:

Mary: 25 John: 35 Ted: 15 Lisa: 45 Anna: 20

Calculate:
a. the harmonic and
b. arithmetic means

Correct result:

h =  24.101
m =  28

Solution:

$$\begin{gathered} n=5 \\ h=n\mathrm{/}(1\mathrm{/}25+1\mathrm{/}35+1\mathrm{/}15+1\mathrm{/}45+1\mathrm{/}20)=5\mathrm{/}(1\mathrm{/}25+1\mathrm{/}35+1\mathrm{/}15+1\mathrm{/}45+1\mathrm{/}20)=24.101 \end{gathered}$$

$m=(25+35+15+45+20)\mathrm{/}n=(25+35+15+45+20)\mathrm{/}5=28$

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